Cryptogram 23

Algebra Level 2

$A$ , $B$ , $C$ , and $D$ each represents a different digit between 1 to 9, such that $\overline{ABCD}$ is a 4-digit number.

If $A \times \overline{AB}=\overline{CD}$ , what is the 3-digit number we get, when we divide $\overline{ABCD}$ by the $\overline{AB}$ ?

\101

\overline{10A}

\overline{11A}

\overline{1AB}

1 solution

Henry U
Feb 12, 2019

$A \cdot \overline{AB} = \overline{CD} \Leftrightarrow \overline{CD} : \overline{AB} = A$

$\begin{aligned} & \overline{ABCD} : \overline{AB} \\ =& (100\overline{AB}+\overline{CD}) : \overline{AB} \\ =& 100\overline{AB} : \overline{AB} + \overline{CD} : \overline{AB} \\ =& 100 + A \\ =& \boxed{\overline{10A}} \end{aligned}$

Cryptogram 23

1 solution

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